Curriculum Vitae
David John Benson
17 March 1993
Work address: Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, England.
Tel: 0865-273570. Email DJB@VAX.OX.AC.UK
Home address: 14 Aldrich Rd., Oxford OX2 7ST, England. Tel: 0865-511454.
Date and Place of Birth: 3rd December 1955, Farnborough, Hampshire, England.
Education and Employment
Dates ||Place ||Degree/Position
_________________________________________________________________________
1986- ||University of Oxford ||University Lecturer and fellow
| |of Wolfson College
| |
1984- 86 ||Northwestern University, ||Assistant Professor
|Evanston, IL, USA |(NSF grant held)
| |
1982- 84 ||Yale University, New Haven, ||Gibbs Instructor
|CT, USA |(NSF grant held)
| |
1981- 82 ||Arhus Universitet, Danmark ||Royal Society exchange fellow
1978- 81 ||Trinity College, Cambridge ||Ph. D. in Mathematics
1977- 78 |Trinity College, Cambridge |Part III Mathematics, honours
| |with distinction
|| ||
1974- 77 |Trinity College, Cambridge |First class honours in Mathe-
| |
| |matics tripos
| |
| |Entrance Scholar
| |Senior Scholar
| |
| |Yeats Essay Prize
| |
1967- 74 ||Maidstone Grammar School ||8 O-levels, 3 A/S-levels
| |(Mathematics A1, Physics A,
| |
| |Chemistry A1)
| |
Sabbatical leave: September to December 1990, invited visitor for the progr*
*am on
Representations of Finite Groups, MSRI, Berkeley, California, USA.
September to December 1991, School of Mathematics, University of Minnesota, *
*Min-
neapolis, USA.
1
Ph. D. Thesis
Supervisor: Prof. J. G. Thompson.
Subject: Finite group theory.
Title: The Simple Group J4.
Date Received: 12th June, 1982.
Current Research Interests
Cohomology of groups, modular representation theory, algebraic topology, invari*
*ant theory
for finite groups.
Publications
[1]The Simple Group J4. Ph. D. Thesis, Cambridge 1982.
[2]The Loewy structure of the projective indecomposable modules for A8 in char*
*acteris-
tic 2. Comm. in Algebra 11 (13) (1983), 1395-1432.
MR84k:20006a, ZB528.20007
[3]The Loewy structure of the projective indecomposable modules for A9 in char*
*acteris-
tic 2. Comm. in Algebra 11 (13) (1983), 1433-1453.
MR84k:20006b, ZB528.20008
[4](with R. A. Parker.) The Green ring of a finite group. J. Algebra 87 (1984)*
*, 290-331.
MR86a:16013, ZB539.20009
[5]Lambda and psi operations on Green rings. J. Algebra 87 (1984), 360-367.
MR86g:16013, ZB539.20011
[6]Modular representation theory: New trends and methods. Springer Lecture
Notes in Mathematics 1081, Springer-Verlag, Berlin/New York 1984. (231 pp.)
MR86g:20013, ZB564.20004
[7](with J. H. Conway.) Diagrams for modular lattices. J. Pure & Appl. Algebra*
* 37
(1985), 111-116.
MR87b:06018, ZB575.06008
[8]Brauer trees for 12M22. J. Algebra 95 (1985), 398-408.
MR87d:20030, ZB574.20009
[9]Some recent trends in modular representation theory. Proceedings of the gro*
*up theory
year at Rutgers, C.U.P. 1985, 249-259.
MR86j:20003, ZB648.20014
2
[10](with W. Feit and R. Howe.) Finite linear groups, the Commodore 64, Euler a*
*nd
Sylvester. Amer. Math. Monthly 93 (9) (1986), 717-719.
MR87m:05011, ZB611.10013
[11]Modules for finite groups: representation rings, quivers and varieties. (Th*
*ree lectures
given at the Fourth International Conference on the Representations of Alge*
*bras)
Representation Theory II, Groups and Orders, Ottawa 1984. Springer Lecture *
*Notes
in Mathematics 1178, 1-24. Springer-Verlag, Berlin/New York 1986.
MR87m:20031
[12](with J. F. Carlson.) Nilpotent elements in the Green ring. J. Algebra 104 *
*(1986),
329-350.
MR88b:20021, ZB612.20005
[13]Representation rings of finite groups. (Two lectures given at the 1985 Durh*
*am Sym-
posium on the Representations of Algebras) Representations of Algebras, Dur*
*ham
1985. London Math. Soc. Lecture Note Series 116, 181-199. C.U.P., 1986.
MR88i:16037, ZB621.20003
[14](with J. F. Carlson.) Diagrammatic methods for modular representations and *
*coho-
mology. Comm. in Algebra 15 (1&2) (1987), 53-121.
MR87m:20032, ZB615.20032
[15](with N. Habegger.) Varieties for modules and a problem of Steenrod. J. Pur*
*e & Appl.
Algebra 44 (1987), 13-34.
MR88e:55020, ZB617.55005
[16](with J. F. Carlson.) Complexity and multiple complexes. Math. Zeit. 195 (1*
*987),
221-238.
MR88e:20050, ZB608.20041
[17]Some remarks on the decomposition numbers for the symmetric groups. The Arc*
*ata
Conference on Representations of Finite Groups, Proc. Symp. Pure Math. Amer.
Math. Soc. 47, Part 1 (1987), 381-394.
MR89b:20037, ZB654.20010
[18]Spin modules for symmetric groups. J. London Math. Soc. (2) 38 (1988), 250-*
*262.
MR89k:20020, ZB669.20005
[19]Projective modules for the group of the twenty-seven lines on a cubic surfa*
*ce. Comm.
in Algebra 17 (5) (1989), 1017-1068.
MR90d:20022, ZB678.20003
3
[20]Cyclic homology and path algebra resolutions. Math. Proc. Camb. Phil. Soc. *
*106
(1989), 57-66.
MR90f:18010, ZB677.16014
[21](with J. F. Carlson and G. R. Robinson.) On the vanishing of group cohomolo*
*gy.
J. Algebra 131 (1990), 40-73.
MR91c:20073, ZB697.20043
[22](with L. Evens.) Isomorphisms in finite group cohomology. Comm. in Algebra *
*18
(1990), 3447-3452.
MR91h:20080
[23]Representations and Cohomology, Vol. I: Basic representation theory of
finite groups and associative algebras. (xi + 224 pp.) Cambridge Studies in
Advanced Mathematics 30, Cambridge University Press, 1991.
MR92m:20005, ZB718.20001
[24]Representations and Cohomology, Vol. II: Cohomology of groups and mod-
ules. (x + 278 pp.) Cambridge Studies in Advanced Mathematics 31, Cambridge
University Press, 1991.
[25](with S. Martin.) Mod 2 cohomology of the unitary groups U3(2n). Comm. in A*
*lgebra
19 (1991), 3125-3144.
MR93a:20072
[26](with V. Franjou.) Series de composition de modules instables et injectivit*
*e de la
cohomologie du groupe Z=2. Math. Zeitschrift 208 (1991), 389-399.
MR93b:55022, ZB725.55012
[27](with F. R. Cohen.) Mapping class groups of low genus and their cohomology.
(iv + 104 pp.) Memoirs of the Amer. Math. Soc. 443, 1991.
MR91g:57002, ZB732:57003
[28](with M. Feshbach.) Stable splittings of classifying spaces of finite group*
*s. Topology
31 (1992), 157-176.
[29]Resolutions and Poincare duality for finite groups. In: Proceedings of the *
*June 1990
Barcelona conference on Homotopy and Group Cohomology. Springer Lecture Not*
*es
in Mathematics 1509, Springer-Verlag, Berlin/New York 1992.
[30](with J. F. Carlson.) Projective resolutions and Poincare duality complexes*
*. To appear
in Trans. Amer. Math. Soc.
[31](with J. F. Carlson.) The cohomology of extraspecial groups. Bull. London M*
*ath. Soc.
24 (1992), 209-235.
MR93b:20087
4
[32](with J. F. Carlson.) Periodic modules with large period. Quarterly Journal*
* of Math-
ematics 43 (1992), 283-296.
[33](with J. F. Carlson.) Products in negative cohomology. J. Pure & Appl. Alge*
*bra 82
(1992), 107-129.
[34]The image of the transfer. To appear in Archiv der Mathematik, 1993.
[35](with M. Feshbach.) On the cohomology of split extensions. To appear in Pro*
*c. Amer.
Math. Soc., 1993.
[36](with J. Greenlees.) The action of the Steenrod algebra on Tate cohomology.*
* To appear
in J. Pure & Appl. Algebra.
[37]Poincare series for the cohomology of compact Lie groups. Preprint, 1992.
[38](with J. F. Carlson.) Functional equations for Poincare series in group coh*
*omology.
Submitted to the Journal of the London Math. Soc., 1992.
[39]Polynomial Invariants of Finite Groups. (v + 126 pp.) To appear, L.M.S. Lec-
ture Notes in Mathematics, C.U.P., 1993.
[40](with W. W. Crawley-Boevey.) A ramification formula for Poincare series, an*
*d a
hyperplane formula for modular invariants. Preprint, 1993.
[41](with J. Wood.) Integral invariants and cohomology of BSpin(n). In preparat*
*ion.
[42](with J. F. Carlson.) Cohomology of the double cover of the Mathieu group M*
*12. In
preparation.
[43]Simplicial and Cosimplicial Homotopy Theory. Printed lecture notes, Oxford,*
* 1993.
Book reviews
[44]C. W. Curtis and I. Reiner. Methods of Representation Theory, with Appli-
cations to Finite Groups and Orders, Volume II. (Wiley & Sons Ltd., 1987)
Bull. London Math. Soc. 20 (1988), 535-542.
Graduate Students
John Fitzgerald June '87 - Oct '90
Title of thesis: Weyl modules for groups of type B2 and G2.
Laurence Barker Oct '87 - Jun '89, Apr '90 - Dec '91
Title of thesis: Blocks of endomorphism algebras of modules.
Paul Day Oct '88 -
5
Subject: The May spectral sequence for group algebras.
Jon Clark Oct '90 -
Subject: Cohomology of nilpotent groups of class two.
Dan Brown Jun '91 -
Subject: Relative cohomology of finite groups.
Katrina Hicks Apr '92 -
Subject: Representation theory.
Teaching Experience
Cambridge University (undergraduate supervisions, 1978-1981)
Group theory
Representation theory
Algebraic geometry
Galois theory
Number theory
First year algebra and analysis
Second year complex variables
Yale University
1982-3 : (undergraduate)
Calculus 112 (Differentiation)
Calculus 115 (Integration)
(graduate)
Modular representation theory
1983-4 : (undergraduate)
Early Concentration Mathematics for Freshmen
(Topics included: ordinary differential equations,
Fourier series and Fourier transforms, and some analytic number the*
*ory)
(graduate)
Ordinary representations of finite Chevalley groups
Northwestern University
1984-5 : (undergraduate)
B20 Calculus of several variables
A11 Finite mathematics
(graduate)
E11-1 Integral and modular representation theory
6
1985-6 : (undergraduate)
C35 Number theory
(graduate)
D46-1 Algebraic topology: Homotopy theory
D46-3 Topological K-theory
University of Oxford
1986-7 : (graduate)
Representation theory and cohomology of groups I, II
1987-8 : (3rd year undergraduate)
Representation theory of finite groups
(graduate)
Representations of algebras
1988-9 : (graduate)
Representation theory and cohomology of finite groups I, II, III
1989-90 : (graduate)
Block theory
Introduction to algebraic geometry
1990-1 : (graduate)
Commutative algebra I: Intersection theory
Commutative algebra II: Invariant theory
1991-2 : (3rd year undergraduate)
Representation theory of finite groups
(graduate)
Classifying spaces of finite groups
(seminar)
Cohomology of groups seminar (2 terms)
1992-3 : (graduate)
Simplicial and cosimplicial homotopy theory (2 terms)
Invited lectures
"The simple group J4." Conference, Oberwolfach, West Germany: Gruppentheorie,*
* 27
April-3 May 1980.
"The Green ring of a finite group." Conference, Paris VII, France: Theorie de*
*s blocs,
7
June 1982.
"Diagrams for modular lattices." Conference, Oberwolfach, West Germany: Darstel*
*lungs-
theorie endlicher Gruppen, 24-30 July, 1983.
"Modules for finite groups." Three lectures. Conference, Troisieme Cycle Roma*
*nd de
Mathematique, Les Plans sur Bex, Switzerland: Representations des groupes finis*
*, March
1984.
"Modules for finite groups: representation rings, quivers and varieties." Thre*
*e lectures.
Fourth International Conference on the Representations of Algebras, Ottawa, Can*
*ada,
16-25 August, 1984.
"Nilpotent elements in representation rings." Algebra seminar, University of I*
*llinois at
Urbana-Champagne, U.S.A., December 1984.
"Representation rings of finite groups." Conference, Northwestern University, *
*Illinois,
U.S.A: Cohomology of groups. March 1985.
"Representation rings of finite groups." Two lectures. Durham (U.K.) symposium:*
* Rep-
resentations of Algebras, 15-25 July, 1985.
"Semidihedral groups and Bott periodicity." Conference, Oberwolfach, West Germ*
*any:
Topologische Methoden in der Gruppentheorie, 1-7 June, 1986.
"Representation rings." Conference, Arcata, California, U.S.A: Representations *
*of finite
groups and related topics. 6-25 July, 1986.
"Spin modules for symmetric groups." Conference, Arcata, California, U.S.A: Rep*
*resen-
tations of finite groups and related topics. 6-25 July, 1986.
"Specht modules and the cohomology of mapping class groups." Conference, Oberwo*
*lfach,
West Germany: Darstellungstheorie endlicher Gruppen, 31 May-6 June 1987.
"Cyclic homology and block theory." Representation theory seminar, Manchester, *
*U.K.,
March 1988.
"Astronomical clocks, continued fractions and the back wheels of a car." Invari*
*ant Society,
Oxford, U.K., 24 May, 1988.
"Cyclic homology of path algebras." Conference, Marseille-Luminy, France: Hom*
*otopy
Theory, July 1988.
"On the vanishing of group cohomology." Topology seminar, University of Kentuck*
*y, Lex-
ington, U.S.A., September 1988.
Three lectures: "Specht modules and the cohomology of mapping class groups," "O*
*n the
vanishing of group cohomology," and "How to build a sporadic group." Universit*
*y of
Minneapolis, Minnesota, U.S.A., September 1988.
Group theory seminar: "The Evens norm map and Steenrod operations in group coho-
mology," and K-theory seminar (Karoubi): "Stable splittings of classifying spac*
*es of finite
groups." Paris, France, March 1989.
8
"The Evens norm map and Steenrod operations in group cohomology." Representati*
*on
theory seminar, Universit"at Essen, West Germany, April 1989.
Two lectures: "Poincare duality and cohomology of finite groups," and "Stable s*
*plittings
of classifying spaces of finite groups." Universite de Geneve, Switzerland, Apr*
*il 1989.
"Projective resolutions and complexes." Conference, Arcata, California, U.S.A: *
*Represen-
tations of finite and related algebraic groups. 8-14 July, 1989.
"Projective resolutions of modules for finite groups." Arhus Universitet, Octo*
*ber 1989
and Kobenhaven Universitet, Denmark, October 1989.
"The classifying space of a finite group." Colloquium, Birmingham University, *
*U.K.,
November 1989.
"Projective resolutions of modules for finite groups." ETH Z"urich, Switzerland*
*, January
1990.
"Representations and cohomology of finite groups." British Mathematics Colloqu*
*ium,
Norwich, U.K., April 1990.
"Resolutions and Poincare duality for finite groups." Barcelona conference on h*
*omotopy
theory, Spain, 6-12 June 1990.
"Mapping class groups of surfaces of low genus and their cohomology." Universit*
*y of Vir-
ginia at Charlottesville, U.S.A., joint Algebra/Topology seminar, 11 September *
*1990.
Colloquium: "Reflection groups, braids and mapping class groups," and seminar: *
*"Projec-
tive resolutions of modules for finite groups." University of Illinois at Urban*
*a-Champaign,
Illinois, U.S.A., 11-12 Oct 1990.
"On the Becker-Gottlieb transfer." Topology seminar, University of Minnesota, *
*Min-
neapolis, U.S.A., 24 Oct 1990.
"Projective resolutions of modules for finite groups." Colloquium, University o*
*f Rochester,
New York, U.S.A., 31 Oct 1990.
"Extraspecial groups and modules with large period." Northeast Topology Meeting*
*, Al-
bany, New York, U.S.A., 2 Nov 1990.
"Reflection groups, braids and mapping class groups." Seminar, University of G*
*eorgia,
Athens GA, U.S.A., 8 Nov 1990.
Two lectures: "Projective resolutions of modules for finite groups," and "Extr*
*aspecial
groups and modules with large period." Conference on representations of finite*
* groups,
MSRI Berkeley, California, U.S.A., Dec 1990.
"Reflection groups, braids and mapping class groups." Colloquium, Liverpool Uni*
*versity,
U.K., 22 Feb 1991.
"Why are most products zero in negative degree cohomology?" Algebra seminar, C*
*am-
bridge University, U.K., 4 March 1991.
"Products in negative cohomology." Representation theory meeting, Warwick Unive*
*rsity,
9
U.K., 6 June 1991.
"The image of the transfer." Seminar, Universit"at G"ottingen, Germany, 7 Augus*
*t 1991.
"Why are most products zero in negative degree cohomology?" Conference on class*
*ifying
spaces of compact Lie groups, G"ottingen, 12 Sept 1991.
"The image of the transfer." Group theory seminar, University of Chicago, U.S.*
*A., 24
Oct 1991.
"Why are most products zero in negative degree cohomology?" Midwest Group Theory
Meeting, University of Chicago, U.S.A., 26 Oct 1991.
"The transfer map in group cohomology." Colloquium, University of Virginia at *
*Char-
lottesville, U.S.A., 12 Dec 1991.
"The image of the transfer." Algebra Seminar, Yale University, New Haven CT, U.*
*S.A.,
1 April 1992.
"Why are most products zero in negative Tate cohomology?" Algebra Seminar, Univ*
*ersity
of Virginia at Charlottesville, U.S.A., 14 April 1992.
"Polynomial invariants of finite groups." Colloquium, University of Virginia a*
*t Char-
lottesville, U.S.A., 16 April 1992.
"The index of a module for a finite group." Invited talk at the summer meeting*
* of the
Canadian Math. Society, Toronto, Canada, 12 June 1992.
"Projective resolutions and Poincare duality for finite and compact Lie groups.*
*" Seminar,
University of Rochester, New York, U.S.A., 17 June 1992.
"Poincare duality in the cohomology of the classifying spaces of finite and com*
*pact Lie
groups." Invited lecture at the Amer. Math. Soc. 1992 Summer Research Conferenc*
*e on
Cohomology, Representations and Actions of Finite Groups, South Hadley, Massach*
*usetts,
U.S.A., 25 June 1992.
Four lectures on the cohomology of finite groups, University of Virginia at Cha*
*rlottesville,
U.S.A., September 1992.
"The transfer map in group cohomology." Colloquium, Bristol University, U.K., 8*
* Decem-
ber 1992.
"On the cohomology of finite groups." Colloquium, Sheffield University, U.K., 2*
*4 February
1993.
Musical Activities
Playing the flute since 1975
Singing (bass) since 1987
Playing the piano since 1988
10
Choral Concerts
Brahms: A German Requiem. Oxford Harmonic Society, Sun 26 Nov 1989, Oxford
Town Hall, with the Oxford Symphony Orchestra, conducted by Brian Trowell.
J. S. Bach: Mass in B minor. Oxford Harmonic Society, Sat 17 March 1990, She*
*ldonian
Theatre, Oxford, with the Guildhall Chamber Orchestra, conducted by Brian Trowe*
*ll.
Beethoven: Choral Symphony. Oxford Harmonic Society, Thu 3 June 1990, Ded-
dington Church, Oxfordshire, with the Oxford Symphony Orchestra, conducted by B*
*rian
Trowell.
Gilbert and Sullivan: Trial by Jury, and Elgar part songs: Deep in my soul (*
*Op. 53 No.
2), Owls (Op. 53 No. 4), There is sweet music (Op. 53 No. 1) and O wild west wi*
*nd (Op.
53 No. 3). Oxford Harmonic Society, Wed 23 June 1990, Holywell music room, Oxfo*
*rd,
conducted by Brian Trowell.
J. Haydn: St. Nicholas Mass, and Bruckner: two motets, Ave Maria and Ecce sa*
*cer-
dos. Worcester/Somerville Choral Society, Oxford, Sat. 2 Mar 1991, St. Aloysius*
* church,
Oxford.
E. Elgar: The Dream of Gerontius. Oxford Harmonic Society, Sat. 23 Mar 199*
*1,
Sheldonian Theatre, Oxford, with the Oxford Symphony Orchestra, conducted by Ro*
*bert
Secret.
Charpentier: Te Deum. Oxford Classical Chorus, Sat 8 June 1991, Keble Coll*
*ege
Chapel, Oxford, with the Oxford Classical Orchestra, directed by Neil Farrow an*
*d Hilary
Norris.
Berlioz: Requiem. Oxford Harmonic Society, Wed 12 June 1991, Sheldonian Thea*
*tre,
Oxford, with the Oxford Symphony Orchestra, conducted by Robert Secret.
Mozart: Mass in B flat K. 427, Regina Coeli K. 127, Litaniae K. 243. Unive*
*rsity
of Minnesota Chamber Singers, director Thomas Lancaster, with the Concert Choir*
* and
Chamber Orchestra, conducted by Murray Sidlin. Mon Nov. 18, 1991, Calvary Luthe*
*ran
Church, Golden Valley, Minnesota; Tue Nov. 19, College of St. Benedict, St. Jos*
*eph,
Minnesota (this performance was recorded and played on National Public Radio on*
* Sun
Dec. 8); Tue Dec. 3, Northrup Auditorium, University of Minnesota.
Vivaldi: Gloria, Doyle: Non Nobis Domine, Balfour Gardiner: Evening Hymn, Tc*
*hai-
kovsky: The Crown of Roses. Kodaly Choir, Sat 28 Nov. 1992, Merton College Chap*
*el,
Oxford, conducted by Anna Smith.
Mendelssohn: Elijah. Oxford Harmonic Society, Sun 14 March 1993, Oxford To*
*wn
Hall, with the Oxford Symphony Orchestra, conducted by Robert Secret.
Operatic Choral R^oles
Mozart: Idomeneo. Oxford University Opera Club, 1-4 May 1991 (four fully sta*
*ged
performances with period instruments), Playhouse, Oxford, conducted by Jonathan*
* Wil-
liams and produced by Alison Brown.
11
Tchaikovsky: Eugene Onegin. Oxford University Opera Club, 6-9 May 1992 (four*
* fully
staged performances), Playhouse, Oxford, conducted by Duncan Hinnells and produ*
*ced
by Rosie Johnston.
12